Problem: Solve for $x$ : $2x^2 + 34x + 144 = 0$
Solution: Dividing both sides by $2$ gives: $ x^2 + {17}x + {72} = 0 $ The coefficient on the $x$ term is $17$ and the constant term is $72$ , so we need to find two numbers that add up to $17$ and multiply to $72$ The two numbers $8$ and $9$ satisfy both conditions: $ {8} + {9} = {17} $ $ {8} \times {9} = {72} $ $(x + {8}) (x + {9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 8) (x + 9) = 0$ $x + 8 = 0$ or $x + 9 = 0$ Thus, $x = -8$ and $x = -9$ are the solutions.